Finite Group Databasebeta

← #26232525

Subgroups — #26232525

Order 12032.

1226 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689821C211yesmaximal, characteristic
2C2×C8×C22⋊D47C211yesmaximal, characteristic, complemented
3#20246313C211yesmaximal, characteristic, complemented
4#20244351C211yesmaximal, characteristic, complemented
5#20244342C211yesmaximal, characteristic, complemented
6#20243816C211yesmaximal, characteristic, complemented
7#20243815C211yesmaximal, characteristic, complemented
8#20243709C211yesmaximal, characteristic, complemented
9#20243705C211yesmaximal, characteristic, complemented
10#20243482C211yesmaximal, characteristic, complemented
11#20243478C211yesmaximal, characteristic, complemented
12#20243397C211yesmaximal, characteristic, complemented
13#20243202C211yesmaximal, characteristic, complemented
14#20243103C211yesmaximal, characteristic, complemented
15C2×C47×#340C211yesmaximal, characteristic, complemented
16C22×C8×D47C2211yescharacteristic
17#15689821—24no—
18#15689821C418yescomplemented
19C2×#13094019—21no—
20C2×#13094015C2211yescharacteristic
21C2×#13094009—21no—
22C2×#13093999C2211yescharacteristic
23C2×#13093998—21no—
24C2×#13093998C2211yescharacteristic
25C2×#13093986C2211yescharacteristic
26C2×C4×C22⋊D47—21no—
27C2×C4×C22⋊D47C2211yescharacteristic
28C2×#13093982C2211yescharacteristic
29C2×#13093982C2211yescharacteristic
30C8×C22⋊D47—24no—
31C2×Dic47⋊C8C2211yescharacteristic
32C2×#13093946C2211yescharacteristic
33C2×#13093946C2211yescharacteristic
34C2×#13093944C2211yescharacteristic
35C2×#13093944C2211yescharacteristic
36C2×C22⋊(C47⋊C8)C2211yescharacteristic
37C2×(C2×D47)⋊C8C2211yescharacteristic
38C2×C8×Dic47C2211yescharacteristic
39#15689013—21no—
40#15689004—21no—
41#15689002—21no—
42#15688988C2211yescharacteristic
43#15688983C2211yescharacteristic
44#15688980C2211yescharacteristic
45C4⋊C4×Dic47C2211yescharacteristic
46C4×C22⋊Dic47—21no—
47#15688886C2211yescharacteristic
48#15688886C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688885C2211yescharacteristic
51#15688885C2211yescharacteristic
52#15688885C2211yescharacteristic
53#15688885C2211yescharacteristic
54#15688885C2211yescharacteristic
55C23×C8×C47C2211yescharacteristic
56C22×C4⋊C4×C47C2211yescharacteristic
57C22×C4⋊C4×C47C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C22×D188—21no—
63C22×D188C2311yescharacteristic
64C22×C22⋊D47—21no—
65C22×C22⋊D47D411yescharacteristic
66C22×C4×D47—21no—
67C22×C4×D47C2311yescharacteristic
68C22×C47⋊C8C2311yescharacteristic
69C22×C47⋊C8C2311yescharacteristic
70C2×C8×D47—22no—
71C2×C8×D47—22no—
72C2×C8×D47—41no—
73#13094019—28no—
74#13094015—22no—
75#13094015C2×C414yescomplemented
76#13094009—28no—
77#13093999—22no—
78#13093999C2×C414yescomplemented
79#13093998—22no—
80#13093998—28no—
81#13093998C2×C414yes—
82#13093986—22no—
83#13093986C2×C414yescomplemented
84C4×C22⋊D47—28no—
85C4×C22⋊D47C2×C414yes—
86C4×C22⋊D47D414yes—
87#13093982—22no—
88#13093982—22no—
89#13093982—41no—
90#13093982C2×C414yescomplemented
91C2×C4⋊Dic47—21no—
92C2×C4⋊Dic47C2311yescharacteristic
93C2×C4⋊Dic47C2311yescharacteristic
94C2×C4⋊Dic47C2311yescharacteristic
95C2×Dic47⋊C4—21no—
96C2×Dic47⋊C4D411yescharacteristic
97C2×C22⋊Dic47—21no—
98C2×C22⋊Dic47D411yescharacteristic
99C2×(C2×D47)⋊C4—21no—
100C2×(C2×D47)⋊C4—21no—
101C2×(C2×D47)⋊C4—21no—
102C2×(C2×D47)⋊C4—21no—
103C2×(C2×D47)⋊C4—21no—
104C2×(C2×D47)⋊C4—21no—
105C2×(C2×D47)⋊C4D411yescharacteristic
106C2×C4×Dic47—21no—
107C2×C4×Dic47—21no—
108C2×C4×Dic47—21no—
109C2×C4×Dic47C2311yescharacteristic
110Dic47⋊C8—22no—
111#13093946—22no—
112#13093946—41no—
113#13093944—22no—
114#13093944—41no—
115C22⋊(C47⋊C8)—22no—
116(C2×D47)⋊C8—22no—
117C8×Dic47—22no—
118C47⋊#95—21no—
119C47⋊#95—21no—
120C47⋊#95—21no—
121C47⋊#95—21no—
122C47⋊#95—21no—
123C23×C4×C47—21no—
124C23×C4×C47—21no—
125C23×C4×C47C2311yescharacteristic
126C22×C8×C47—22no—
127C22×C8×C47—22no—
128C22×C8×C47—41no—
129C22×C8×C47C2311yescharacteristic
130C22×C8×C47C2311yescharacteristic
131C2×C4⋊C4×C47—22no—
132C2×C4⋊C4×C47—21no—
133C2×C4⋊C4×C47—22no—
134C2×C4⋊C4×C47—21no—
135C2×C4⋊C4×C47—41no—
136C2×C4⋊C4×C47C2×C414yes—
137C2×C4⋊C4×C47C2311yescharacteristic
138C2×C4⋊C4×C47C2311yescharacteristic
139C2×C4⋊C4×C47C2311yescharacteristic
140C2×C4⋊C4×C47C2311yescharacteristic
141C24×C47C2×D411yescharacteristic
142C23×D47—21no—
143C23×D47C2×D411yescharacteristic
144C22×C4×C47—21no—
145C22×C4×C47—21no—
146C22×C4×C47—21no—
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—24no—
152C22×C4×C47—21no—
153C22×C4×C47—42no—
154C22×C4×C47—42no—
155C22×C4×C47—81no—
156C22×C4×C47—81no—
157C22×C4×C47—81no—
158C22×C4×C47C22×C412yes—
159C22×C4×C47C2×D411yescharacteristic
160C22×C4×C47C2×D412yes—
161C22×C4×C47C2411yescharacteristic
162C2×C22⋊D47—22no—
163C2×C22⋊D47—22no—
164C2×C22⋊D47—24no—
165C2×C22⋊D47—42no—
166C2×C22⋊D47—42no—
167C2×C22⋊D47C22⋊C414yes—
168C22×Dic47—21no—
169C22×Dic47—21no—
170C22×Dic47—21no—
171C22×Dic47C2×D411yescharacteristic
172C22×Dic47C2×D411yescharacteristic
173C22×Dic47C2×D411yescharacteristic
174C2×D188—21no—
175C2×D188—21no—
176C2×D188—21no—
177C2×D188—21no—
178C2×D188—21no—
179C2×D188—24no—
180C2×D188—81no—
181C2×D188—81no—
182C2×D188C22×C412yes—
183C2×C4×D47—21no—
184C2×C4×D47—21no—
185C2×C4×D47—21no—
186C2×C4×D47—21no—
187C2×C4×D47—24no—
188C2×C4×D47—81no—
189C2×C4×D47—81no—
190C2×C4×D47C22×C412yes—
191C2×C4×D47C2×D412yes—
192C2×C8×C47—21no—
193C2×C8×C47—21no—
194C2×C8×C47—21no—
195C2×C8×C47—21no—
196C2×C8×C47—21no—
197C2×C8×C47—44no—
198C2×C8×C47#4112yes—
199C4⋊C4×C47—24no—
200C4⋊C4×C47—21no—
201C4⋊C4×C47—21no—
202C4⋊C4×C47—21no—
203C4⋊C4×C47—21no—
204C4⋊C4×C47—21no—
205C4⋊C4×C47—42no—
206C4⋊C4×C47C22×C412yes—
207C4⋊C4×C47C22×C412yes—
208C4⋊C4×C47#4112yes—
209C22⋊Dic47—42no—
210C22⋊Dic47C22⋊C414yes—
211(C2×D47)⋊C4—24no—
212(C2×D47)⋊C4—24no—
213(C2×D47)⋊C4—24no—
214(C2×D47)⋊C4—24no—
215(C2×D47)⋊C4—42no—
216(C2×D47)⋊C4—81no—
217(C2×D47)⋊C4C22⋊C414yes—
218C4⋊Dic47—21no—
219C4⋊Dic47—24no—
220C4⋊Dic47—21no—
221C4⋊Dic47—21no—
222C4⋊Dic47—21no—
223C4⋊Dic47—21no—
224C4⋊Dic47C22×C412yes—
225Dic47⋊C4—24no—
226Dic47⋊C4C22⋊C414yes—
227C4×Dic47—24no—
228C4×Dic47—42no—
229C4×Dic47—81no—
230C4×Dic47C22×C412yes—
231C4×Dic47C2×D412yes—
232C2×C47⋊C8—21no—
233C2×C47⋊C8—21no—
234C2×C47⋊C8—21no—
235C2×C47⋊C8—21no—
236C2×C47⋊C8—21no—
237C2×C47⋊C8—21no—
238C8×D47—44no—
239C23×C47—21no—
240C23×C47—21no—
241C23×C47—21no—
242C23×C47—21no—
243C23×C47C2×C22⋊C412yes—
244C23×C47#13512yes—
245C23×C47#13512yes—
246C23×C47C22×D411yescharacteristic
247C22×D47—21no—
248C22×D47—21no—
249C22×D47—21no—
250C22×D47—21no—
251C22×D47—21no—
252C22×D47—21no—
253C22×D47—22no—
254C22×D47—41no—
255C22×D47—41no—
256C22×D47—41no—
257C22×D47—41no—
258C22×D47—41no—
259C22×D47—41no—
260C22×D47C2×C22⋊C412yes—
261C2×C4×C47—21no—
262C2×C4×C47—21no—
263C2×C4×C47—22no—
264C2×C4×C47—22no—
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—22no—
268C2×C4×C47—22no—
269C2×C4×C47—22no—
270C2×C4×C47—41no—
271C2×C4×C47—41no—
272C2×C4×C47—41no—
273C2×C4×C47—41no—
274C2×C4×C47—41no—
275C2×C4×C47—41no—
276C2×C4×C47—41no—
277C2×C4×C47—41no—
278C2×C4×C47—41no—
279C2×C4×C47—84no—
280C2×C4×C47—84no—
281C2×C4×C47C2×C22⋊C412yes—
282C2×C4×C47C23×C411yescharacteristic
283C2×C4×C47C22×D411yescharacteristic
284C2×C4×C47C2×#4111yescharacteristic
285C2×C4×C47C2×#4111yescharacteristic
286C2×C4×C47H(5,𝔽2)11yescharacteristic
287C2×C4×C472−1+411yescharacteristic
288C22⋊D47—28no—
289C22⋊D47—48no—
290C2×Dic47—21no—
291C2×Dic47—21no—
292C2×Dic47—21no—
293C2×Dic47—21no—
294C2×Dic47—21no—
295C2×Dic47—21no—
296C2×Dic47—22no—
297C2×Dic47—41no—
298C2×Dic47—41no—
299C2×Dic47—41no—
300C2×Dic47—41no—
301C2×Dic47—41no—
302C2×Dic47—41no—
303C2×Dic47—41no—
304C2×Dic47—41no—
305C2×Dic47C2×C22⋊C412yes—
306C2×Dic47C2×C22⋊C412yes—
307C2×Dic47C2×C22⋊C412yes—
308D188—22no—
309D188—22no—
310D188—41no—
311D188—41no—
312D188—84no—
313C4×D47—22no—
314C4×D47—22no—
315C4×D47—22no—
316C4×D47—22no—
317C4×D47—84no—
318C8×C47—22no—
319C8×C47—41no—
320C47⋊C8—41no—
321C47⋊C8—41no—
322#22488—471nomaximal, Sylow
323C22×C47—22no—
324C22×C47—22no—
325C22×C47—22no—
326C22×C47—22no—
327C22×C47—22no—
328C22×C47—22no—
329C22×C47#41614yes—
330C22×C47C22×C22⋊C411yescharacteristic
331C22×C47#54611yescharacteristic
332C22×C47#54711yescharacteristic
333C22×C47C2×#13511yescharacteristic
334C22×C47C2×#13511yescharacteristic
335C22×C47#57611yescharacteristic
336C22×C47#57711yescharacteristic
337C2×D47—22no—
338C2×D47—22no—
339C2×D47—22no—
340C2×D47—41no—
341C2×D47—41no—
342C2×D47—41no—
343C2×D47—41no—
344C2×D47—42no—
345C2×D47—42no—
346C2×D47—42no—
347C2×D47—81no—
348C2×D47—81no—
349C2×D47—81no—
350C2×D47—81no—
351C4×C47—22no—
352C4×C47—42no—
353C4×C47—42no—
354C4×C47—42no—
355C4×C47—81no—
356C4×C47C4×#4111yescharacteristic
357C4×C47#52011yescharacteristic
358C4×C47#54611yescharacteristic
359C4×C47#54711yescharacteristic
360Dic47—22no—
361Dic47—22no—
362Dic47—22no—
363Dic47—42no—
364Dic47—81no—
365Dic47—81no—
366C2×#553—471no—
367C2×C8×D4—471no—
368#2352—471no—
369#1991—471no—
370#1989—471no—
371#1893—471no—
372#1893—471no—
373#1875—471no—
374#1874—471no—
375#1825—471no—
376#1824—471no—
377#1804—471no—
378C4×#102—471no—
379#1735—471no—
380C2×#340D4711yescharacteristic, complemented
381C2×C47—24no—
382C2×C47#233911yescharacteristic
383C2×C47C2×#41611yescharacteristic
384C2×C47#289711yescharacteristic
385C2×C47#329711yescharacteristic
386C2×C47#330111yescharacteristic
387C2×C47#333711yescharacteristic
388C2×C47#333911yescharacteristic
389D47—42no—
390D47—82no—
391C23×C8—471no—
392C23×C8C2×D4711yescharacteristic
393#553—478no—
394#553—944no—
395C2×#126—941no—
396C2×#125—471no—
397C2×#123—941no—
398C2×#121—471no—
399C2×#121—471no—
400C2×#121—941no—
401C2×C4×D4—471no—
402C2×C4×D4—471no—
403C2×C4×D4—941no—
404C2×#117—471no—
405C2×#117—471no—
406C22×C4⋊C4C2×D4711yescharacteristic
407C22×C4⋊C4C2×D4711yescharacteristic
408C8×D4—944no—
409C2×C4⋊C8—471no—
410C2×#102—471no—
411C2×#102—471no—
412C2×#102—471no—
413C2×#102—471no—
414C2×C22⋊C8—471no—
415C2×C22⋊C8—471no—
416C2×C4×C8—471no—
417#388—941no—
418#387—941no—
419#386—941no—
420#382—471no—
421#380—471no—
422#380—471no—
423C4×C4⋊C4—471no—
424C4×C22⋊C4—941no—
425#340—471no—
426#340—471no—
427#340—471no—
428#340—471no—
429#340—471no—
430#340—471no—
431#340—471no—
432#340—471no—
433#340C2×D4711yescharacteristic
434#340C2×D4711yescharacteristic
435#340C2×D4711yescharacteristic
436#340C2×D4711yescharacteristic
437C47#2248811yescharacteristic, complemented, Sylow
438C22×D4—471no—
439C22×D4—471no—
440C22×D4—941no—
441C22×D4—941no—
442C23×C4—21no—
443C23×C4—21no—
444C23×C4—471no—
445C23×C4—941no—
446C23×C4C22×D4711yescharacteristic
447C22×C8—22no—
448C22×C8—22no—
449C22×C8—41no—
450C22×C8—471no—
451C22×C8—471no—
452C22×C8—942no—
453C22×C8—942no—
454C22×C8—1881no—
455C22×C8C22×D4711yescharacteristic
456C22×C8C22×D4711yescharacteristic
457#126—948no—
458#125—474no—
459#125—942no—
460#123—948no—
461#121—474no—
462#121—474no—
463#121—942no—
464#121—948no—
465#121—942no—
466C4×D4—474no—
467C4×D4—474no—
468C4×D4—474no—
469C4×D4—942no—
470C4×D4—948no—
471#117—474no—
472#117—942no—
473#117—942no—
474#117—1881no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—41no—
480C2×C4⋊C4—471no—
481C2×C4⋊C4—471no—
482C2×C4⋊C4—471no—
483C2×C4⋊C4—471no—
484C2×C4⋊C4—941no—
485C2×C4⋊C4—941no—
486C2×C4⋊C4C4×D4714yes—
487C2×C4⋊C4C22×D4711yescharacteristic
488C2×C4⋊C4C22×D4711yescharacteristic
489C2×C4⋊C4C22×D4711yescharacteristic
490C2×C4⋊C4C22×D4711yescharacteristic
491C2×C22⋊C4—471no—
492C2×C22⋊C4—471no—
493C2×C22⋊C4—941no—
494C2×C22⋊C4—941no—
495C2×C22⋊C4—941no—
496C2×C22⋊C4—941no—
497C2×C22⋊C4—941no—
498C2×C22⋊C4—941no—
499C2×C22⋊C4—941no—
500C2×C42—471no—
501C2×C42—941no—
502C2×C42—941no—
503C2×C42—941no—
504C4⋊C8—942no—
505#102—942no—
506#102—942no—
507#102—1881no—
508#102—1881no—
509C22⋊C8—942no—
510C22⋊C8—942no—
511C4×C8—942no—
512#95—941no—
513#95—941no—
514#95—941no—
515#95—941no—
516#95—941no—
517C24—471no—
518C24—941no—
519C24D4×D4711yescharacteristic
520C2×D4—474no—
521C2×D4—472no—
522C2×D4—944no—
523C2×D4—942no—
524C2×D4—942no—
525C2×D4—944no—
526C2×D4—941no—
527C2×D4—941no—
528C2×D4—941no—
529C2×D4—941no—
530C2×D4—941no—
531C2×D4—3761no—
532C2×D4—3761no—
533C2×D4—1882no—
534C2×D4—1882no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—24no—
543C22×C4—21no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—81no—
547C22×C4—81no—
548C22×C4—81no—
549C22×C4—471no—
550C22×C4—471no—
551C22×C4—471no—
552C22×C4—472no—
553C22×C4—472no—
554C22×C4—944no—
555C22×C4—941no—
556C22×C4—941no—
557C22×C4—941no—
558C22×C4—941no—
559C22×C4—941no—
560C22×C4—941no—
561C22×C4—941no—
562C22×C4—3761no—
563C22×C4—3761no—
564C22×C4C2×C4×D4712yes—
565C22×C4D4×D4711yescharacteristic
566C22×C4D4×D4712yes—
567C22×C4C23×D4711yescharacteristic
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—44no—
574C2×C8—941no—
575C2×C8—941no—
576C2×C8—941no—
577C2×C8—941no—
578C2×C8—941no—
579C2×C8—941no—
580C2×C8—1884no—
581C2×C8#1062535012yes—
582C4⋊C4—24no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—42no—
589C4⋊C4—474no—
590C4⋊C4—472no—
591C4⋊C4—944no—
592C4⋊C4—944no—
593C4⋊C4—941no—
594C4⋊C4—941no—
595C4⋊C4—941no—
596C4⋊C4—941no—
597C4⋊C4—941no—
598C4⋊C4C2×C4×D4712yes—
599C4⋊C4C2×C4×D4712yes—
600C4⋊C4#1062535012yes—
601C22⋊C4—474no—
602C22⋊C4—474no—
603C22⋊C4—944no—
604C22⋊C4—944no—
605C22⋊C4—944no—
606C22⋊C4—944no—
607C22⋊C4—3761no—
608C22⋊C4—1882no—
609C22⋊C4—1882no—
610C42—472no—
611C42—472no—
612C42—944no—
613C42—3761no—
614C42—1882no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—472no—
620C23—941no—
621C23—941no—
622C23—941no—
623C23—941no—
624C23—941no—
625C23—941no—
626C23—942no—
627C23—1881no—
628C23—1881no—
629C23—1881no—
630C23—1881no—
631C23—1881no—
632C23—1881no—
633C23C22⋊C4×D4712yes—
634C23#1309404512yes—
635C23#1309404712yes—
636C23C2×D4×D4711yescharacteristic
637D4—948no—
638D4—942no—
639D4—942no—
640D4—3764no—
641D4—1888no—
642D4—1881no—
643D4—1881no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—84no—
663C2×C4—84no—
664C2×C4—472no—
665C2×C4—472no—
666C2×C4—472no—
667C2×C4—941no—
668C2×C4—941no—
669C2×C4—941no—
670C2×C4—941no—
671C2×C4—941no—
672C2×C4—941no—
673C2×C4—942no—
674C2×C4—942no—
675C2×C4—942no—
676C2×C4—942no—
677C2×C4—942no—
678C2×C4—3764no—
679C2×C4—1881no—
680C2×C4—1881no—
681C2×C4—1881no—
682C2×C4—1881no—
683C2×C4—1881no—
684C2×C4—1881no—
685C2×C4—1881no—
686C2×C4—1881no—
687C2×C4C22⋊C4×D4712yes—
688C2×C4C22×C4×D4711yescharacteristic
689C2×C4C2×D4×D4711yescharacteristic
690C2×C4C2×#1062535011yescharacteristic
691C2×C4C2×#1062535011yescharacteristic
692C2×C4#1309406911yescharacteristic
693C2×C4#1309407211yescharacteristic
694C8—22no—
695C8—41no—
696C8—1881no—
697C8—1881no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—942no—
705C22—942no—
706C22—942no—
707C22—3761no—
708C22—3761no—
709C22—3761no—
710C22—3761no—
711C22—1882no—
712C22—1882no—
713C22—1882no—
714C22—1881no—
715C22—1881no—
716C22—1881no—
717C22—1881no—
718C22#1568911814yes—
719C22C2×C22⋊C4×D4711yescharacteristic
720C22#1568976311yescharacteristic
721C22#1568977411yescharacteristic
722C22C2×#1309404511yescharacteristic
723C22C2×#1309404711yescharacteristic
724C22#1568992411yescharacteristic
725C22#1568992911yescharacteristic
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—81no—
731C4—942no—
732C4—942no—
733C4—942no—
734C4—3761no—
735C4—3761no—
736C4—1882no—
737C4C4×#1062535011yescharacteristic
738C4#1568960411yescharacteristic
739C4#1568976311yescharacteristic
740C4#1568977411yescharacteristic
741C2—24no—
742C2—3762no—
743C2—1882no—
744C2#2024621511yescharacteristic
745C2C2×#1568911811yescharacteristic
746C2#2025190911yescharacteristic
747C2#2025523411yescharacteristic
748C2#2025528611yescharacteristic
749C2#2025576311yescharacteristic
750C2#2025578611yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#340C2
socleC23×C47C22×D4
prime radicalC2×#15689821C2
cosocleC22×C4×C47C24
hypercenterC2×#340D47
hypocenterC47#22488
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#340

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C8×C22⋊D47C2semidirect
3. #20246313C2semidirect
4. #20244351C2semidirect
5. #20244342C2semidirect
6. #20243816C2semidirect
7. #20243815C2semidirect
8. #20243709C2semidirect
9. #20243705C2semidirect
10. #20243482C2semidirect
11. #20243478C2semidirect
12. #20243397C2semidirect
13. #20243202C2semidirect
14. #20243103C2semidirect
15. C2×C47×#340C2semidirect
18. #15689821C4semidirect
75. #13094015C2×C4semidirect
78. #13093999C2×C4semidirect
83. #13093986C2×C4semidirect
90. #13093982C2×C4semidirect
380. C2×#340D47semidirect
437. C47#22488semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#156898212
C2×C8×C22⋊D472
#202463132
#202443512
#202443422
#202438162
#202438152
#202437092
#202437052
#202434822
#202434782
#202433972
#202432022
#202431032
C2×C47×#3402
#2248847